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Part 4

We all looked over at Kelley, one of the gold traders. She was quoting the Telerate news ticker off the monitor on her desk. There was no further information.

We then looked past Kelley, out the seventh floor windows of 222 Broadway, and down the half block of a side street to No. 4 World Trade Center (WTC). The COMEX, where gold futures are traded, was on the 8th floor of No. 4 WTC, and Kelley and one of the other gold traders had open phones lines to the trading floor.

The background voices at the COMEX, heard over the speakers where we were, sounded normal. The street scene outside looked normal also.

“Why don’t you ask the floor if there’s anything unusual over there,” I suggested to Kelley. We had two brokers on the COMEX floor.

Nothing out of the ordinary, they said. No bomb here. One opined he had felt a small shake of the building. The other one hadn’t noticed even that.

Those of us at 222 Broadway went back to work, filing away this interesting, but seemingly irrelevant piece of information: a bomb at the World Trade Center. It was, in fact, another hour before smoke began to fill the elevators at No. 4 WTC, and COMEX traders were ordered to evacuate the building. In the meantime, Kelley kept us updated as more news hit the ticker.

“It was centered in the garage area,” she announced.

For the first time, someone looked concerned. “I’m parked over there,” he said.

Tom wandered by my desk. “Want to go take a look?” he asked. Tom was a PhD chemist who had turned option trader. He had a natural curiosity about explosions.

I declined the invitation. Where there is one bomb, there may be two, and I preferred to wait until the excitement was over. If the bomb was in the parking garage, I doubted there was anything to see, anyway. Tom shrugged and left by himself. He returned with a report: the bomb had collapsed the lobby floor of the Vista Hotel on the ground floor of the tower at No. 1 WTC, as well as the floor below that, and a 20- foot crater now extended out to the street beside the tower. From our windows, we couldn’t see the activity taking place because No. 4 WTC blocked our view. I reflected that I had passed through the Vista Hotel lobby the previous day, en route to the walkway connecting the World Trade Center to the World Financial Center located on the other (wharf) side of Manhattan’s Westside Highway.

As it turned out, the WTC bomb had been planted by an FBI informant, whose FBI handler had insisted he use real explosives, and not fake that part of the “sting”. This was reported in the New York Times before Louis Freeh’s media handlers went to work and quashed reports of the FBI connection, and diverted all attention to the supposedly purely foreign nature of the “Middle Eastern terrorists” (with U.S. intelligence connections) whose operation the FBI had been assisting under the guise of conducting a “terrorist sting”.

It was claimed the bombers had intended to bring down the tower at No. 1 WTC. Though in fact the van filled with explosive (alleged, but not shown, to be urea nitrate) had done no damage to the building structure. Explosive pressure drops off approximately with the cube of the distance, so to do serious damage with a low-power explosive, you need to attached it to the building columns.

What the explosion had done was to take out two floors in a particular area vertical to the van location, and to fill the building cavities with smoke. Most of the 1000 or so injuries resulted from smoke inhalation, and were basically confined to those taking the commuter trains from New Jersey into the train station in the basement of the WTC. That is, to passers-through trapped in smoke, and not to people actually working at the WTC.

By the end of the day, Tom and I were discussing ANFO bombs instead of options. Where I had grown up in Texas, ammonium nitrate was widely used as fertilizer. It was just one of those things prevalent in the environment, like gasoline and butane, that you used and treated with respect. I had never known anyone killed with ammonium nitrate, although I had known two people, including one neighbor, who had blown themselves up welding “empty” butane tanks.

No, the FBI-assisted terrorists hadn’t done much damage to the World Trade Center, relatively speaking, aside from the Vista Hotel. But for a few hours on Feb. 26, 1993, they had shut down the COMEX, and– London trading having finished for the day–most of the world’s gold market along with it.

Gold Futures

Gold futures are traded at the COMEX in New York (which merged with the NYMEX on August 3, 1994, and is now known as the “COMEX Division” of the New York Mercantile Exchange), at the TOCOM in Tokyo, and–until recently– at the SIMEX in Singapore. Gold futures are also traded at the Chicago Board of Trade (CBOT) and at the Istanbul Gold Exchange. (The latter is mostly a market for spot gold. For example, over 8 million ounces of gold were traded spot at the Istanbul Gold Exchange in 1997, but only about 43,000 ounces were traded through the futures market.)

Gold futures are priced much like the gold forwards we discussed in part 3. That is, in their relationship to the spot price, futures show little difference from forwards. But there are many other ways in which futures contracts differ from forwards, and it is important to understand what these are.

Forward gold is traded for contract settlement at standardized intervals from spot settlement, in intervals that correspond to foreign exchange forward contracts: 1, 2, 3, 6, and 12-month forwards are typical. Spot gold traded on Wednesday June 24 will settle on Friday, June 26. A one-month forward trade on June 24 will take us to July 26, which is a Sunday, so settlement of a one-month forward will be on Monday, July 27. A two-month forward trade on June 24 will take us to August 26, which is a Wednesday, so settlement of a two-month forward contract will be on August 26. And so on.

Futures, by contrast, are traded for fixed dates in the future. At the COMEX and CBOT, gold is traded for settlement in February, April, June, August, October, and December, as well as the current and next two calendar months. Istanbul trades the next six months for Turkish lira-denominated contracts, or the next 12 months for U.S. dollar-denominated contracts. The last trading day for a futures contract is the fourth to last business day in the delivery month (at the CBOT or Istanbul), or the third to last business day (at the COMEX). That is, the August 1998 COMEX gold future trades until the third to last business day in August 1998. At the TOCOM, there are futures for the current or next odd month, and all even months within a year. The last trading day is the third to last business day, except for December, when the last trading day is December 24.

Despite the different trade date conventions, however, if futures and forward settlement dates happen to correspond, forward and futures prices are the same, subject to slight differences related to delivery grade or location (Manhattan, say, versus London).

How Futures Markets Deal with Credit Risk

The main different between futures and forwards is the way futures markets handle credit risk. In the forward market, a credit evaluation must be made of the counterparty–evaluating the counterparty’s ability to pay cash if gold was purchased forward, or the ability to deliver the gold, if gold was sold forward.

The futures market don’t worry about such customer credit evaluations. Instead, a futures contract is configured as a pure bet, based on price change. So one is asked to post a security bond, called “margin”, which covers the typical variation in the value of a contract for several days. Going long a futures contract is a bet that the price is going up, while going short is a bet the price is going down. Cash flows from price changes take place daily. So those who post the required margin against possible losses (and who replenish this margin if necessary) are considered credit-worthy, while those who can’t post margin aren’t credit-worthy. Customers post margin with member firms of the futures exchange, who in turn post margin with clearing member firms. The clearing member firms post margin (on the customer’s behalf) at a clearinghouse. This way of dealing with credit risk is a much cleaner structure than in the forward market world of customer credit evaluations, accounting reports, and other types of intrusive financial reporting. (Of course, exchange member firms and, especially, clearing member firms still have to undergo the usual sorts of credit checks.)

To close out a long position, one sells (goes short) an off-setting contract. To close out a short position, one buys (goes long) an off-setting contract. The opening and subsequent closing of a futures position is referred to as a “round turn”. Brokerage fees are usually charged per round turn, at the time the future contract is closed out.

At discount brokerage firms in the U.S., in June 1998, the typical customer margin on a 100 oz. gold futures contract was about $1350, while there was a typical brokerage charge of $25 per round turn.

The size of the futures bet depends on the stated size of the futures contract. The cash flow will be the change in price multiplied by the contract size.

At the COMEX, CBOT, and the SIMEX, the contract size is 100 ozs of gold with a fineness of .995. So if gold (of that fineness) went from $299/oz at contract opening to $297.50/oz as the day’s futures settlement price, a long contract would lose $150, while a short contract would gain $150. (The calculation on the short position is $299 minus $297.50, multiplied by 100.)

The TOCOM trades 1 kilo bars (32.148 ozs) of .9999 fineness. The price is stated as yen/gram. So the daily change in value of a single contract is the change in the yen price per gram, multiplied by 1000 grams.

The Istanbul gold futures contract is for 3 kilograms of gold of .995 fineness, quoted either in terms of U.S. dollars per ounce, or Turkish lira per gram. The daily change in value of a U.S. dollar- denominated contract is the change in dollars per oz, multiplied by 96.444 ozs. The daily change in value of a Turkish lira-denominated contract is the change in the Turkish lira price per gram, multiplied by 3000 grams.

The “initial” margin that must be posted as a security bond is large enough to cover several days expected/loss or gain, and is thus related to the standard deviation of daily contract value changes. The margin is held by a clearinghouse which thus “guarantees” that the losing side of the daily futures bet pays the winning side. For every customer that goes long a contract, the clearinghouse takes the other side, going short. For every customer that goes short a contract, the clearinghouse takes the other side, going long. The clearinghouse thus is in a position to move cash from the losing side of any futures bet to the winning side.

If the initial margin is depleted by losses, it eventually reaches a “maintenance” margin level, below which the customer is required to replenish the margin to its initial level. For example, at discount brokerage firms in the U.S. in June 1998, a typical maintenance margin level for gold futures contracts at the COMEX was $1000 per contract. So if the posted margin dropped below $1000 per futures contract, additional margin had to be posted to bring the total back to at least $1350 per contract (the typical initial margin level).

Customers typically may post margin in the form of cash, or U.S. government securities with less than 10 years to maturity. Clearing members may post cash, government securities, or letters of credit with the clearinghouse. The details differ at different exchanges.

The Equilibrium Futures Price

The equilibrium futures price is that point where the market clears between longs and shorts. Arbitrage, however, forces the futures price to track the forward price (and vice-versa). Similarly, arbitrage between the futures market and the spot market on the final day of trading forces the futures price to converge to the spot price. On the final trading day at the SIMEX, where no gold can actually be delivered on a futures contract, the settlement price is set as the loco London price of the A.M. London price fix. This forces convergent of the futures price to the price in the London spot market. At the COMEX and CBOT, the open longs take delivery of spot gold, which accomplishes the same thing.

(On January 9, 1998, the SIMEX removed trading of its gold futures contract from the floor of the exchange. The contract is still available on the SIMEX Automated Trading System.)

Delivery at the COMEX and the CBOT is one 100-oz bar (plus or minus 5 percent) or three 1-kilogram gold bars, assaying not less than .995 fineness. (Note that 3 kilo bars is about 96 ounces of gold. The dollar amount actually paid at delivery depends, of course, on the specific amount of gold delivered, which must be within 5 percent of the hypothetical 100 ozs per contract.) Delivery at the CBOT takes place by a vault receipt drawn on gold deposits made in CBOT-approved vaults in Chicago or New York. Gold delivered against futures contracts at the COMEX must bear a serial number and identifying stamp of a refiner approved by the COMEX, and made from a depository located in the Borough of Manhattan, City of New York, and licensed by the COMEX. As noted previously, there is no delivery at the SIMEX. The futures contract is purely cash- settled, with the final settlement price determined by the London A.M. gold fix.

In part 3, we saw the U.S. dollar forward price of gold would be related to the U.S. dollar spot price of gold by the relationship

F(T) = S [1 + r (T/360)] / [1 + r* (T/360)].

where the spot price is S, the forward (or futures) price is F(T) for a time-horizon of T days, the eurodollar rate is r, and the gold lease rate is r*. If the eurodollar rate r is higher than the gold lease rate r*, then the forward (futures) gold price will be higher than the spot gold price. Historically gold lease rates have always been lower than eurodollar rates, so forward gold (or a gold futures contract) always trades at a higher price than spot gold. The same is not true, for example, in the silver market. During the year 1998, silver lease rates have frequently exceeded eurodollar rates, so forward silver has traded at a cheaper price than spot silver.

Different terms are used to refer to the relationship between forward or futures prices and spot prices. If forward gold (or a gold future) has a higher price than spot gold, the forward gold or gold future is said to be at a premium, or (in the London market) in contango. If forward gold has a lower price than spot gold, the forward gold or gold future is at a discount, or (in the London market) in backwardation.

As we noted before, forward gold has in recent history always been in contango, or at a premium, because dollar interest rates have always been above gold lease rates. We saw in part 3 that the difference between the forward price and the spot price, F(T)-S, is the swap rate. Since the forward price of gold has always been at a premium in recent years (since 1980, in particular), the swap rate has always been positive. A related term that is used in the U.S. futures markets is basis. Basis is the spot price minus the futures price, or S-F(T), which is just the swap rate with the sign reversed. The gold basis has always been negative in recent years. The Federal Reserve Bank of Cleveland, for example, publishes monthly charts of the gold basis. Reverse the sign on their chart, and you are looking at the swap rate.

Exchange for Physicals

While forward gold is traded in the form of swaps, which combines a spot trade (buy or sell) with the reverse forward trade (sell or buy), gold futures can be traded in the form of EFPs (exchange for physicals), which combine a futures trade with the reverse spot trade. EFPs are traded for the same months as gold futures. The EFP price represents the difference between the futures price and the spot price for the combined trade.

For example, a marketmaker may quote the August EFP at the COMEX as $1.10-$1.30 in 100 lots. This means the marketmaker’s prices are good for a standard trade involving 100 futures contracts (10,000 ozs of gold). The marketmaker will “buy” the EFP at $1.10/oz, or “sell” the EFP for $1.30/oz.

This quotation implies that for $1.10/oz. the marketmaker offers to buy from you 100 gold futures contracts, while simultaneously selling to you 10,000 ozs of spot gold. For $1.30/oz. the marketmaker will sell to you 100 gold futures contracts, while simultaneously purchasing 10,000 ozs of spot gold. To summarize: the marketmaker’s bid price is the price he will buy futures versus selling spot, while the marketmaker’s asked price is the price he will sell futures versus buying spot. The EFP price is thus simply a different way of looking at the basis or the swap rate.

On June 24, 1998, the mid-market price (average of bid and asked prices) of the EFP associated with the August 1998 COMEX gold contract was a positive $1.25, while the mid-market price associated with the Dec 1998 COMEX gold contract was a positive $5.60. By contrast, the EFP associate with the July 1998 COMEX silver contract was a negative $2.00. This reflected the fact that gold lease rates were below eurodollar rates, while silver lease rates were above.

Interest rates in the gold market are a principal concern of gold dealers and gold mining companies.

In Parts 3 and 4, we saw how two interest rates– gold lease rates and eurodollar rates–determine the relationship between the dollar price of spot gold and the dollar price of gold forwards and futures. In the forward market, these two interest rates give rise to the swap rate, while in the futures market they determine the EFP price. Both swaps and EFPs involve a spot sale or purchase of gold, along with the reverse trade in the forward market (if a swap) or futures market (if an EFP).

Because eurodollar rates have historically always exceeded gold lease rates, gold forward and futures have always traded at a premium (have always been in contango). There is nothing inevitable about this relationship, however.

But there are many contracts in the gold market that do not involve the spot, forward or future price of gold, but rather are simply written in terms of gold interest rates. These include gold forward rate agreements (FRAs), gold interest rate swaps, and gold interest rate guarantees (IRGs). Let’s examine each of these contracts in turn.

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Where Grabbe uses the term eurodollar rate he refers to what we nowadays call the LIBOR interest rate on fiat money. Read gold libor as gold lease rate.

Written by James Orlin Grabbe in the late nineties.

Part 3

Now that we have seen how spot gold is priced “loco London,” we can examine how other local markets, and other types of gold contracts, are priced in reference to the London spot market. This includes other spot delivery locations, gold forward and futures contracts — such as the gold futures contract at the NYMEX in New York — and gold swaps, forward rate agreements, and options. (In 1994 the COMEX merged with the NYMEX, and the principal gold futures contract now trades there.)

London is only one of many important centers for gold trading. The second principal center for spot or physical gold trading, for example, is Zurich. For eight hours a day, trading occurs simultaneously in London and Zurich — with Zurich normally opening, and closing, an hour earlier than London. During these hours Zurich closely rivals London in its influence over the spot price, because of the importance of the three major Swiss banks — Credit Suisse, Swiss Bank Corporation, and Union Bank of Switzerland — in the physical gold market. Each of these banks has long maintained its own refinery, often taking physical delivery of gold and processing it for other regional markets.

(On December 8, 1997, Swiss Bank Corporation and Union Bank of Switzerland announced plans to merge, the combined bank to be known as United Bank of Switzerland. The net effect such a merger would ultimately have on the Zurich gold market is not yet clear.)

In addition to other gold delivery locations, there are other weight and quality standards which create differential prices. Examples include the London and Tokyo kilobars (which are 32.148 ozs., instead of the circa 400 oz. “large bars”), the 10 tola bars (3.75 ozs.) popular in India and the Middle East, the 1, 5 and 10 tael bars (respectively 1.203, 6.017, and 12.034 ozs.) found in Hong Kong and Taiwan, and the baht bar (0.47 ozs) of Thailand. Gold content is another difference. The London good delivery bar is only required to have a minimum of 995 parts gold to 1000 parts total. But a gold content of 9,999 parts gold to 10,000 parts total (“four nines”) is commonly traded, as is a content of 990 parts to 1,000 total (the baht bar being an example of the latter ratio). Gold purity is important to industry. Jewellers might want gold in the form of grain for alloying, while electronics firms may require “five nines” — meaning .99999 purity.

Pricing Nonstandard Contracts

Nonstandard contracts can be priced by reference to the standard loco London good delivery bar, by taking into account the simple arbitrage relationships that would turn one into another. The primary variables to keep track of are the costs of shipping gold from one location to another, the cost of refining gold to different purity levels, and the interest or financing cost for the time required to accomplish these activities.

Suppose a dealer is offered non-good delivery bars of .995 purity loco Panama City. Here is one chain of calculations the dealer might go through to come up with a price quotation. First the dealer notes that London good delivery bars of .9999 purity can be sold in Tokyo for $.50/oz premium to the standard loco London price. He knows that if he buys the bars in Panama, he could sell them in Tokyo, but first he would have to ship them to an appropriate location to upgrade their purity.

The dealer also knows that he can upgrade to London large bars for good delivery, and have the gold content refined to .9999 purity, for $.50/oz at the Johnson Matthey refinery in Salt Lake City, Utah. There is a two-week turnaround time for the upgrade. Shipping time is one day from Panama City to Salt Lake, and two days from Salt Lake to Tokyo.

The dealer calculates the cost of shipping and insurance from Panama to Salt Lake as $.40/oz, while shipping from Salt Lake to Tokyo is $.70/oz. The total time consumed would be 15 days, which at 6 percent interest and spot gold at, say, $300/oz amounts to 300 x .06 (15/360) = $.75/oz.

Therefore the dealer’s best, or break-even, quotation to the person offering him non-standard gold bars in Panama City would be the spot price for good delivery loco London minus $1.85. If spot gold were at $300/oz. bid, the most the dealer could afford to bid for the Panama bars would be $298.15/oz.

The Gold Lease or Gold Libor Rates

Gold bears interest. Positive interest. Many people do not know this. They are used to the notion of storing their gold with some bank or warehouse, and paying for storage cost. They then view the storage and insurance cost as a negative interest rate. But this has little to do with the way gold is priced or traded in the wholesale market.

The forward price of gold — the price agreed now for gold to be purchased or sold at some time in the future — is a function of the gold spot price, and the interest rates representing alternative uses of resources over the forward time period. So before we discuss gold forward prices, we should discuss gold and dollar interest rates.

This brings us to the gold lease rate, or the gold interest rate paid on gold deposits. Another term that is used is gold libor, by analogy with the London Interbank Offered Rate for eurocurrencies traded in London. Despite the apparent literal connotation of each of these labels, “gold libor rates” and “gold lease rates” are alternative descriptions that refer to the bid-asked gold interest rates paid on gold. The bid rate (deposit rate, borrowing rate) is the gold interest rate paid for borrowing gold (that is, on gold deposits), while the asked or offered rate is the gold interest rate quoted for lending gold. The expressions “bid-asked gold lease rates” or “bid-asked gold libor rates” are thus interchangeable.

If the gold borrowing rate is 2 percent per annum, for example, then 100 ozs of gold borrowed for 360 days must be repaid as 102 ozs of gold. (Gold interest rates, like most money market rates, are nearly always quoted on the basis of a 360-day year.) In the early 1980s gold deposits rarely yielded over 1 percent, but in recent years have rarely yielded less than 1 percent.

Because of large central bank gold holdings, gold loans are one of the cheapest financing sources for the gold mining industry. A mining company borrows gold and sells it on the spot market to obtain funds for gold production. The interest installments on the gold loan are payable in gold. And when the loan matures, the principal (and any final interest due) is repaid directly from mine production.

Central banks are the major lenders of gold. They accounted for around 75 percent of the gold on loan, estimated at around 2,750 tonnes, at the end of 1996. Central banks in recent years have been under pressure to earn a return on their gold holdings, and therefore lend to, for example, gold dealers who have mismatched books between gold deposits and gold loans. (The practice of central bank gold lending first became newsworthy in 1990, when the investment banking firm Drexel, Burnham, Lambert went bankrupt while owing borrowed gold to the Central Bank of Portugal.)

The gold lending (or borrowing) rate, then, is one of the components that determine the gold forward price. Let’s see how this works.

The Gold Forward Price

Suppose the spot price of gold is $300/oz. The gold lease rate for 180 days is 2 percent per annum. And the eurodollar rate for 180 days is 6 percent per annum. (For simplicity here, we ignore all bid-asked spreads. But they are easily included in the following calculations.)

I borrow $300 at the eurodollar rate. In 180 days I will have to repay the dollar borrowing with interest in the amount $300 (1+.06(180/360)) = $300 (1.03) = $309.

With the borrowed money I can buy 1 oz. of gold, and place it on deposit for 180 days. The amount of gold I will get back is 1 (1+.02(180/360) = 1 (1.01) = 1.01 oz.

Thus, 1 oz. of gold with a spot price of $300 has grown into 1.01 ounces in 180 days, with a value of $309. This translates into a 180-day forward value of $309/1.01 = $305.94.

Spot price: $300.00

180-day Forward Price: $305.94
Notice that both the gold lease and the eurodollar rate have gone into this calculation. Specifically:

$305.94 = $300 [1+.06 (180/360)] / [1+.02 (180/360)].

In general, if the spot price is S, the forward price is F(T) for a time-horizon of T days (up to a year), the eurodollar rate is r, and the gold lease rate is r*, we have the relation

F(T) = S [1 + r (T/360)] / [1 + r* (T/360)].

Notice that in the numerical example we just used, the forward price $305.94 is approximately 2 percent higher than the spot price of $300. That is, the 180- day forward premium of $5.94 is approximate 2 percent of the spot price of $300. (An exact 2 percent would be $6.) Why is this?

To see what is involved, let’s subtract the spot rate S from both sides of the above equation. The left- hand side will be the forward premium F(T) – S. Simplifying the right-hand side, we obtain:

F(T) – S = S [( r – r*)( T/360)] / [1 + r* (T/360)].

That is, the forward premium (F(T)-S) is approximately equal to the spot rate S multiplied by the difference between the eurdollar rate r and the gold lease rate r* (once we have adjusted this rate for the fraction of a year: T/360).

Since in the numerical example the eurodollar rate was 6 percent, while the least rate was 2 percent, the forward premium at an annual rate is approximately 6-2 = 4 percent. For 180 days, or half a year, it is approximately 2 percent.

So, as long as we are talking about an annual rate — that is, before we do the days adjustment — the gold forward premium in percentage terms is approximately the difference between the eurodollar rate and the gold lease rate.

We can view this same relationship in other ways: given a eurodollar rate and a gold forward premium (in percentage terms), we can back out the implied lease rate.

Looking back at the chart from Kitco, above, it is easy to see that subtracting the gold lease rate from the “prime rate” gives us approximately the gold forward rate. (Note that “prime rate” is a misleading term to use: the relevant interest rate in the gold market is the eurodollar rate by which banks borrow and lend among themselves, not the commercial “prime” lending rate — which is often an administered, rather than a market, interest rate.)

Gold forward rates are sometimes referred to as “GOFO” rates, because GOFO was the Reuters page that showed gold forward rates.

Gold Swaps

There are many different hedging and trading operations in the gold market, all of which bring us back to the same relationship between forward and spot rates we saw in the previous section.

For example, gold dealers will buy gold forward from mining companies. The mining companies, thus assured of a fixed forward price at which to sell their production, go to work producing. Meanwhile, the gold dealers, to hedge themselves against movements in the gold price, borrow gold and sell it in the spot market. (To repeat, dealers “borrow” gold by taking in gold deposits, and paying out the gold lease rate.)

Restated, gold dealers buy gold forward from mining companies at a price F(T). To hedge themselves, the dealers borrow gold at an interest rate r*, and sell it in the market at a price S. They earn interest on the dollar proceeds of the spot gold sale at an interest rate r.

Thus, for each ounce of gold purchased, the dealer must pay

F(T) [1+ r* (T/360) ].

While for each ounce of gold sold, the dealer earns:

S [1 + r (T/360)].

All excess profit (beyond bid-asked spread) gets eliminated when these amounts are equal. Which gives

F(T) [1+ r* (T/360) ] = S [1 + r (T/360)].

This is, of course, exactly the same formula as before.

Generally speaking, gold dealers will quote forward prices to their customers (these are called “outright” forwards), but forward trades beween dealers mostly take place in connection with a simultaneous spot transaction. That is, in the form of “swaps.” A swap transaction is a spot sale of gold combined with a forward repurchase, or a spot purchase of gold combined with a forward sale. This type of trading requires less capital and is subject to less price risk. The swap rate is F(T)-S, and as we saw before, this difference is (when quoted as a percentage of the spot price) essentially the difference between the eurodollar rate and the gold lease rate.

A spot sale of gold combined with a forward purchase is also called a cash-and-carry transaction. The transaction provides immediate cash, the cost of which is the carry, or the difference between forward and spot rates. The dollar lender (who buys the gold), meanwhile has possession of the gold as security. So a cash-and-carry (one form of a swap) boils down to a dollar loan collateralized with gold.

The typical dealing spread between eurodollar deposits is 1/8 of 1 percent, or .125 percent, while the typical spread between gold deposit and loan rates is .20 percent. This translates into bid-asked swap rate, or cash-and-carry, spreads of about .30 percent. For example:

Note that the gold swap rate can be independently viewed as the collateralized borrowing rate. A small central bank, for example, with plenty of gold to spare, could borrow dollars for 3 months and pay — not the 3-month asked eurodollar rate of 3.25 percent — but rather the gold swap rate of 2.70 percent.

James Orlin Grabbe

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